I have a lawn that is mostly moss and ground moles by the truck load. The house blocks most of the sun.?

sorry to say it but your lawn will always have moss, simply because it in the shade, as for the moles i would light a fire making lots of smoke get a vacuum cleaner and suck the smoke. as it comes out of the vacuum exhaust. funnel it down the mole run, and smoke them out

I just sprayed Lilly miller moss out on my mossy lawn and I haven't see any new mole dirt mounds Ina couple days. I am hoping that that might have done the trick

To be honest, I would consider laying interlocking brick. Have some nice flower beds with some ornamental bushes, and a great patio set. My mother had a back yard similar to your description, and she just couldn't get the grass to grow decently without the proper amount of sunlight.

There are chemicals available but be very careful if you have children or outdoor pets as the stuff is nasty. There are probably "green" alternatives available with a bit of web research.